• Structural Engineering and Mechanics
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• 제39권4호
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• pp.541-558
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• 2011

This paper presents an analysis of stochastic eigenvalue problem of plane bar structures. Particular attention is paid to the effect of spatial variations of the flexural properties of the structure on the first four eigenvalues. The problem of spatial variations of the structure properties and their effect on the first four eigenvalues is analyzed in detail. The stochastic eigenvalue problem was solved independently by stochastic finite element method (stochastic FEM) and Monte Carlo techniques. It was revealed that the spatial variations of the structural parameters along the structure may substantially affect the eigenvalues with quite wide gap between the two extreme cases of zero- and full-correlation. This is particularly evident for the multi-segment structures for which technology may dictate natural bounds of zero- and full-correlation cases.

• Structural Engineering and Mechanics
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• 제8권6호
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• pp.579-589
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• 1999

A new way to reduce the eigenvalue computation effort in structural dynamics is presented in this paper. The degrees of freedom of a structure may be classified into groups that are termed as sub-degrees of freedom. The eigenvalue analysis is performed with each of sub-degrees of freedom so that the computing time is much shortened. Since the dynamic coupling between sub-degrees of freedom is selected to be small and it may be considered as a perturbation, the perturbation algorithm is used to obtain an accuratae result. The accuracy of perturbation depends on the coupling between sub-degrees of freedom. The weaker the coupling is, the more accurate the result is. The procedure can be used to simplify a problem of three dimensions to that of two dimensions or from two dimensions to one dimension. The application to a truss and a space frame is shown in the paper.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2009년도 추계학술대회 논문집
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• pp.759-760
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• 2009

• 대한전자공학회논문지
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• 제23권4호
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• pp.455-459
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• 1986

A large set of linear equations which arise in many applications, such as in digital signal processing, image filtering, estimation theory, numerical analysis, etc. involve the problem of a tridiagonal matrix. In this paper, the determinant, eigenvalue and inverse matrix of a tridiagoanl matrix are analytically evaluated.

• 대한기계학회논문집A
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• 제38권6호
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• pp.683-689
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• 2014

본 연구에서는 구조해석 시뮬레이션을 통해 저주파 스퀼을 유발하는 여러 요소를 분석하였다. 해석을 위한 프로그램은 ABAQUS 를 사용하였으며 동적 불안정성을 판명하기 위한 방법으로는 복소 고유치 해석을 채택하였다. 스퀼 유발 요소와 관련된 핵심적인 5 가지 인자를 선정하였고 각각 3 수준으로 분류하였다. 이를 분석하기 위해 실험계획법을 적용하였고, 파라미터 영향도 분석에는 평균분석을 적용하였다. 이을 통해 영향도가 큰 인자를 선별하였고 타당한 해석 기법 및 파라미터 영향분석을 수행하였다.

• Structural Engineering and Mechanics
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• 제52권5호
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• pp.1051-1067
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• 2014

The structures of concern in this study are subject to two types of forces: dead loads from the acceleration imposed on the structures as well as the installed operation machines and the additional adjustable forces. We wish to determine the critical values of the adjustable forces when buckling of the structures occurs. The mathematical statement of such a problem gives rise to a constrained eigenvalue problem (CEVP) in which the dominant eigenvalue is subject to an equality constraint. A numerical algorithm for solving the CEVP is proposed in which an iterative method is employed to identify an interval embracing the target eigenvalue. The algorithm is applied to four engineering application examples finding the critical loads of a fixed-free beam subject to its own body force, two plane structures and one wide-flange beam using shell elements when acceleration force is present. The accuracy is demonstrated using the first example whose classical solution exists. The significance of the equality constraint in the EVP is shown by comparing the solutions without the constraint on the eigenvalue. Effectiveness and accuracy of the numerical algorithm are presented.

• 대한기계학회논문집A
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• 제26권6호
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• pp.1169-1177
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• 2002

A study of fee vibration of circular Mindlin plates is presented. The analysis is based on the pseudospctral method, which uses Chebyshev polynomials and Fourier series as basis functions. It Is demonstrated that rapid convergence and accuracy as well as the conceptual simplicity could be achieved when the pseudospectral method was apt)lied to the solution of eigenvalue problems. Numerical examples of circular Mindlin plates with clamped and simply supported boundary conditions are provided for various thickness-to-radius ratios.

• Structural Engineering and Mechanics
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• 제4권3호
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• pp.277-301
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• 1996

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

• 소음진동
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• 제10권4호
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• pp.648-654
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• 2000

A procedure to determine the realizable optimal positions of rigid supports is suggested to get a maximum fundamental natural frequency. a measured frequency response function based substructure-coupling technique is used to model the supported structure. The optimization procedure carries out the eigenvalue sensitivity analysis with respect to the stiffness of supports. As a result of such stiffness optimization, the optimal rigid-support positions are shown to be determined by choosing the position of the largest stiffness. The optimally determined support conditions are verified to satisfy the eigenvalue limit theorem. To demonstrate the effectiveness of the proposed method, the optimal support positions of a plate model are investigated. Experimental results indicate that the proposed method can effectively find out the optimal support conditions of the structure just based on the measured frequency response functions without any use of numerical model of the structure.

• Journal of the Korean Statistical Society
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• 제30권4호
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• pp.585-595
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• 2001

A second-order response surface model is often used to approximate the relationship between a response factor and a set of explanatory factors. In this article, we deal with canonical analysis in response surface models. For the interpretation of the geometry of second-order response surface model, standard errors and confidence intervals for the eigenvalues of the second-order coefficient matrix play an important role. If the confidence interval for some eigenvalue includes 0 or the estimate of some eigenvalue is very small (near to 0) with respect to other eigenvalues, then we are able to delete the corresponding canonical factor. We propose a formulation of criterion which can be used to select canonical factors. This criterion is based on the IMSE(=Integrated Mean Squared Error). As a result of this method, we may approximately write the canonical factors as a set of some important explanatory factors.